diff --git a/jedi/api/file_name.py b/jedi/api/file_name.py
index 11994074..1787613c 100644
--- a/jedi/api/file_name.py
+++ b/jedi/api/file_name.py
@@ -17,6 +17,8 @@ def complete_file_name(inference_state, module_context, start_leaf, string,
     like_name_length = len(os.path.basename(string))
 
     addition = _get_string_additions(module_context, start_leaf)
+    if string.startswith('~'):
+        string = os.path.expanduser(string)
     if addition is None:
         return
     string = addition + string
diff --git a/test/test_api/test_completion.py b/test/test_api/test_completion.py
index 7d5d183f..545c0242 100644
--- a/test/test_api/test_completion.py
+++ b/test/test_api/test_completion.py
@@ -1,4 +1,4 @@
-from os.path import join, sep as s, dirname
+from os.path import join, sep as s, dirname, expanduser
 import os
 import sys
 from textwrap import dedent
@@ -7,6 +7,7 @@ import pytest
 
 from ..helpers import root_dir
 from jedi.api.helpers import start_match, fuzzy_match
+from jedi._compatibility import scandir
 
 
 def test_in_whitespace(Script):
@@ -86,6 +87,18 @@ def test_loading_unicode_files_with_bad_global_charset(Script, monkeypatch, tmpd
     s.complete(line=2, column=4)
 
 
+def test_complete_expanduser(Script):
+    possibilities = scandir(expanduser('~'))
+    non_dots = [p for p in possibilities if not p.name.startswith('.') and len(p.name) > 1]
+    item = non_dots[0]
+    line = "'~%s%s'" % (os.sep, item.name)
+    s = Script(line, line=1, column=len(line)-1)
+    expected_name = item.name
+    if item.is_dir():
+        expected_name += os.path.sep
+    assert expected_name in [c.name for c in s.completions()]
+
+
 def test_fake_subnodes(Script):
     """
     Test the number of subnodes of a fake object.